Min søster følger et dansk kursus om aftenen, selvom hun arbejder hele dagen.

Yes, the basic meaning of følger is follows, but in this context følger et kursus means takes / attends a course.

So:

• følge en person = follow a person
• følge et kursus = take/attend a course

This is a very common use in Danish, even though it sounds a bit different from English.

Because søster is a common-gender noun in Danish, and common-gender nouns take en and possessives like min.

• en søster
• min søster

If the noun were neuter, you would use mit instead:

• et hus
• mit hus

Because kursus is a neuter noun.

In Danish, every noun is either:

• common gender → takes en
• neuter → takes et

So:

• et kursus
• kurset = the course

This is something you usually just have to learn together with the noun.

In Danish, words for languages, nationalities, and related adjectives are normally not capitalized.

So Danish writes:

• dansk
• engelsk
• tysk

Where English writes:

• Danish
• English
• German

That is completely normal in Danish spelling.

This is because dansk is one of the adjectives that does not add -t here, even though the noun kursus is neuter.

Compare:

• et stort hus → stor becomes stort
• et dansk kursus → dansk stays dansk

So the correct form here is:

• en dansk bog
• et dansk kursus
• danske bøger

Not always 100% definitely.

Et dansk kursus can mean a Danish course, but if you want to be very clear that it is a course in the Danish language, Danish often uses:

• et kursus i dansk = a course in Danish
• et danskkursus = a Danish course / Danish-language course

So your sentence is understandable, but et kursus i dansk is often the clearest way to say it.

Because om aftenen means something like in the evening / in the evenings, often as a regular time.

• om aftenen = in the evening / in the evenings
• i aften = tonight / this evening

So here, the sentence means she does this in the evenings, not specifically tonight.

This is part of a common Danish time expression.

Danish often uses:

• om morgenen = in the morning
• om dagen = during the day
• om aftenen = in the evening
• om natten = at night

So even though English often uses no article in these expressions, Danish commonly uses the definite form.

Hele dagen means the whole day or all day.

After hele, Danish very often uses the definite form:

• hele dagen = the whole day
• hele ugen = the whole week
• hele året = the whole year

So hele dagen is the normal Danish way to say all day.

Because selvom introduces a subordinate clause:

• main clause: Min søster følger et dansk kursus om aftenen
• subordinate clause: selvom hun arbejder hele dagen

In Danish, subordinate clauses are normally separated with a comma in writing. So the comma here is standard.

Because selvom introduces a subordinate clause, and subordinate clauses normally have subject + verb order.

So:

• selvom hun arbejder hele dagen = although she works all day

In a main clause, Danish usually has verb-second word order, but after a subordinating conjunction like selvom, you do not use that main-clause inversion pattern.

It most naturally describes a habit or a regular situation.

The present tense in Danish can be used for:

• things happening now
• regular actions
• general facts

Here, because of om aftenen and hele dagen, the sentence sounds like a repeated routine:

• she attends a Danish course in the evenings
• even though she works all day

Yes. All of these can work, but they are used a bit differently:

• følger et kursus = follows/takes a course
• tager et kursus = takes a course
• går på et kursus = goes to/attends a course

In this sentence, følger et kursus is perfectly natural. A learner should just remember that Danish often uses følge where English would say take or attend.